Roberto Martinez felt the 4-1 scoreline at Arsenal was a harsh reflection on Everton’s performance.
The Blues were in with a shout of at least a replay for much of the quarter-final after Romelu Lukaku cancelled out Mesut Ozil’s early goal.
Mikel Arteta’s penalty put Arsenal back ahead midway through the second half before Olivier Giroud completed the scoring with two quick-fire goals late on.
“It’s hard to take but we lost a tie giving everything and trying to win,” Martinez said.
“The scoreline at the end doesn’t reflect what happened in the game. It shows what we have in the dressing room, trying to go forward right until the final whistle.
“We weren’t happy with the first goal and we need to be much better with our defensive duties. But once we steadied ourselves after the first 20 minutes we were where we wanted to be.
“Unfortunately, we couldn’t score that second goal to put the game in our favour.”
Indeed, Martinez said the contest swung the home side’s way with two key moments when the game was evenly poised at 1-1.
Ross Barkley fired narrowly over the bar before Arsenal regained the lead through Arteta’s spot-kick.
Martinez continued: “I felt it was a situation where Gareth was fighting for the ball with Oxlade-Chamberlain. Of course there was contact but was there enough contact to give a penalty?
“They are difficult decisions and you need luck to be in your favour. Then, from our point of view, there was the chance before that.
“We wanted to make it an open game and have the opportunities to score the second goal. Nine out of 10 times Ross always hits the target from those positions.”